You are given three positive integers N,x,yN,x,y. Please calculate how many permutations of 1∼N1∼N satisfies the following conditions (We denote the ii-th number of a permutation by pipi):
1. p1=xp1=x
2. pN=ypN=y
3. for all 1≤i<N1≤i<N, |pi−pi+1|≤2
Input
The first line contains one integer TT denoting the number of tests.
For each test, there is one line containing three integers N,x,yN,x,y.
* 1≤T≤50001≤T≤5000
* 2≤N≤1052≤N≤105
* 1≤x<y≤N
Output
For each test, output one integer in a single line indicating the answer modulo 998244353998244353.